On the Recognition of Properties of Three-Dimensional Pictures.

In recent years, there have arisen many requirements for three-dimensional 3D data processing with advances in computer tomography CT. Some topological properties of 3D digital pictures have been discussed in a series of papers by Rosenfeld and Morgenthaler, as well as others. A 3D picture can be represented by a 3D array of volume elements voxels for short. In a binary-valued 3D picture each voxel is 0 or 1, it is easy to define connectedness, and objects and cavities are then defined as the equivalence classes of the connectedness relation. These correspond to two-dimensional 2D objects and holes, respectively. Moreover, in the 3D case, there also exist 3D holes whose properties are quite different from those of 2D holes. In this paper, we consider the problem of recognition of the above-mentioned properties of 3D pictures. First, we propose algorithms which for every binary 3D digital picture compute the numbers of objects, cavities and holes. These algorithms are performed in one pass they are 3D versions of the algorithm for 2D digital pictures which was given by Selkow.